Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
150 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26038817 | C2 | semidirect |
| 5. #26038259 | C2 | semidirect |
| 6. #26038254 | C2 | semidirect |
| 7. #362×C179 | C2 | semidirect |
| 72. C179 | #2214 | semidirect |
| 80. #362 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038882 | 2 |
| #26038880 | 2 |
| #26038817 | 2 |
| #26038555 | 2 |
| #26038259 | 2 |
| #26038254 | 2 |
| #362×C179 | 2 |
| #2214 | 179 |